SOAN 3120 - Homework Assignment #2

Kyra Dukovac 1191950 SOAN 3120 Instructor R. Broll Homework Assignment #2 Question 1) → 95% EXAMINE VARIABLES=alwdvwky /PLOT BOXPLOT STEMLEAF /COMPARE GROUPS /STATISTICS DESCRIPTIVES /CINTERVAL 95 /MISSING LISTWISE /NOTOTAL. Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Weekly alcohol consumption 54 32.4% 112 67.6% 166 100.0% Descriptives Statistic Std. Error Weekly alcohol consumption Mean 3.05 .837 95% Confidence Interval for Mean Lower Bound 1.37 Upper Bound 4.73 5% Trimmed Mean 2.20 Median 1.00 Variance 37.695 Std. Deviation 6.140 Minimum 0 Maximum 37 Range 37 Interquartile Range 2 Skewness 2.641 .325 Kurtosis 7.040 .640

→ Analyze To estimate the best population parameter for weekly alcohol consumption at the 95% confidence level, you can use the mean and confidence interval provided in the table. The mean weekly alcohol consumption is 3.05, and the 95% confidence interval for the mean is between 1.37 and 4.73. This means that we can be 95% confident that the true population mean falls within this interval. To determine whether the average Canadian's alcohol consumption is below the two-drink recommendation, you can compare the lower bound of the confidence interval (1.37) with the recommendation of no more than two drinks per week. If the lower bound is less than 2, then it suggests that the average Canadian's alcohol consumption is below the recommendation. In this case, the lower bound of the confidence interval (1.37) is indeed less than 2. Therefore, at a 95% confidence level, it can be inferred that the average Canadian's alcohol consumption is below the two-drink recommendation. → 99.9% EXAMINE VARIABLES=alwdvwky /PLOT BOXPLOT STEMLEAF /COMPARE GROUPS /STATISTICS DESCRIPTIVES /CINTERVAL 99.9 /MISSING LISTWISE /NOTOTAL. Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Weekly alcohol consumption 54 32.4% 112 67.6% 166 100.0% Descriptives Statistic Std. Error Weekly alcohol consumption Mean 3.05 .837 99% Confidence Interval for Mean Lower Bound .81 Upper Bound 5.29

increasing the confidence level is the broader interval, indicating increased confidence but with a wider range for the population parameter, yet the overall conclusion remains consistent. Question 2a) (RECODING) Classr DATASET ACTIVATE DataSet1. RECODE incdghh (5=3) (1 thru 2=1) (3 thru 4=2) INTO classr. VARIABLE LABELS classr 'social class - recoded '. EXECUTE. 1 = Lower class 2 = Middle class 3 = Upper class Lifestressr RECODE gen_020 (3=2) (1 thru 2=1) (4 thru 5=3) INTO lifestressr. VARIABLE LABELS lifestressr 'percieved life stress - recoded'. EXECUTE. 1 = Not stressful 2 = A bit stressful 3 = Stressful Question 2b) Using the Five Step Model → Step 1: Make assumptions and meet test requirements → Model: Random Samples → Level of Measurement: Ordinal In statistical terms, there is an expected statistically significant association between social class and satisfaction with stress, primarily influenced by the complex interplay of socio-economic factors that impact stress management. To reach a definitive conclusion, statistical analysis will be essential, with outputs providing confirmation. It is reasonable to estimate that social class plays a significant role in determining stress satisfaction. Meeting crucial prerequisites for this analysis includes obtaining a random and representative sample, ensuring independence of observations, and using appropriate measurements for social class and stress satisfaction. Adequate sample size and suitable hypothesis tests, such as chi-squared tests, will be used to reject the null hypothesis. → Step 2: State the null hypothesis

Hypothesis: Does a statistically significant correlation exist between an individual's social class and their level of satisfaction with their stress? :µ = The variables are independent 𝐻 0 : µ = The variables are dependent 𝐻 1 → Step 3: Select the sampling distribution and establish the critical region Sampling distribution = (Chi Square) 𝑋 2 Alpha = 0.05 (corresponds with confidence interval of 95%) df = (r - 1) (c - 1) = (3 - 1) (3 - 1) = (2)(2) = 4 (critical) = 9.488 → found in appendix c 𝑋 2 CROSSTABS /TABLES=lifestressr BY classr /FORMAT=AVALUE TABLES /STATISTICS=CHISQ /CELLS=COUNT /COUNT ROUND CELL. percieved life stressor - recoded * social class - recoded Crosstabulation Count social class - recoded Total lower class middle class upper class perceived life stressor - recoded not stressful 9 25 11 45 Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent eved life stressor - recoded * social class ded 166 100.0% 0 0.0% 165.946 100.0%

Question 2c) CROSSTABS /TABLES=lifestressr BY classr /FORMAT=AVALUE TABLES /STATISTICS=GAMMA D BTAU /CELLS=COUNT /COUNT ROUND CELL. Directional Measures Value Asymptotic Standard Error a Approximate T b Approximate Significance Ordinal by Ordinal Somers' d Symmetric -.003 .022 -.117 .907 percieved life stress - recoded Dependent -.003 .022 -.117 .907 social class - recoded Dependent -.002 .021 -.117 .907 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. Symmetric Measures Value Asymptotic Standard Error a Approximate T b Approximate Significance Ordinal by Ordinal Kendall's tau-b -.003 .022 -.117 .907 Gamma -.004 .034 -.117 .907 N of Valid Cases 1730 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. The gamma value of -0.004 corresponds to a 0.4% association strength. Gamma is a scale that ranges from -1.00 (indicating a perfect negative association) to +1.00 (indicating a perfect positive association). A gamma value of -0.004 signifies a weak negative relationship, suggesting that as perceived stress levels increase, social class tends to decrease. This implies that individuals in lower social classes are generally more stressed than those in higher social classes, although the relationship is statistically weak.

Regarding Somers' D and Kendall's Tau B, both measures have values of -0.003. These measures also vary between -1.00 (indicating a negative relationship) and +1.00 (indicating a perfect association). A value of -0.003 implies that the relationship between the variables, while statistically weak, moves in opposite directions. As social class increases, stress levels tend to decrease slightly.